Effective shear viscosity from the friction term in relativistic multi-fluid hydrodynamics

Within a three-fluid description of heavy-ion collisions, we investigate how nuclear friction can be used to model shear stress. In this multi-fluid approach, the individual fluids (projectile, target and fireball) are each treated as locally equilibrated ideal fluids at all times, while the local energy-momentum tensor of the superposed system exhibits characteristic anisotropies in its Landau rest frame. From the corresponding non-vanishing shear stress densities and the gradients of the Landau velocity field, we infer an ``effective shear viscosity’’ according to the Navier-Stokes relation. We present the time evolution of the resulting values of ${\eta }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ and the generated entropy density in nuclear collisions at different beam energies ($1.23A\text{GeV}\le E_{\mathrm{l}\mathrm{a}\mathrm{b}}\le 29.7A\text{GeV}$). The resulting dimensionless ratio ${\eta }_{\mathrm{e}\mathrm{f}\mathrm{f}}\mathrm{/}s$ is determined dynamically and self-consistently within the non-equilibrium friction model. We discuss the relation to previous calculations using alternative methods in hydrodynamics and to estimates based on microscopic transport models.